Systems and methods for determining strand position in a post-tensioned tendon

ABSTRACT

In one embodiment, systems and methods for determining the positions of strands in a post-tensioned tendon involve positioning a magnet in close proximity to the outer surface of a tendon, moving the magnet around the periphery of the tendon, and measuring the force of attraction between the magnet and strands within the tendon at multiple angular positions of the tendon.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application claims priority to U.S. Provisional Application Ser.No. 61/761,960, filed Feb. 7, 2013, which is hereby incorporated byreference herein in its entirety.

BACKGROUND

Post-tensioned construction is a construction technique in whichportions of a structure, such as a bridge, are secured to each otherusing “tendons” that extend throughout the structure. The tendonscomprise an outer duct through which steel strands extend. Once thetendons have been placed into position, the strands are tensioned toprovide rigidity to the structure.

In order to prevent corrosion of the steel strands and improvemechanical performance, the ducts are filled with a grout material,which typically comprises a mixture of cement and water. When the groutis properly distributed within the duct, it creates a chemicalenvironment that protects the steel. When the grout is not properlydistributed, however, corrosion can occur. For example, if air gapsexist within the duct, the portions of the strands within those portionsare exposed and may corrode. Alternatively, if the grout is not mixedproperly or the mixture separates, regions that only contain water canbe formed, which also can lead to corrosion.

There are various methods that can be used to determine if there is aproblem with the grout within a duct. For example, there areelectromagnetic methods that can be used to measure the dielectricproperties of the grout mixture. Acoustic and thermal methods may befeasible as well. Unfortunately, the results that are obtained by suchmethods can depend upon the position of the strands within the duct. Forexample, one may obtain a false negative result (negative meaning thegrout is not deficient) even if the grout is faulty if the testing isperformed on a side of the duct at which the strands are bunchedtogether. Alternatively, an erroneous positive indication of adeficiency (that is, a false positive) may be obtained if the testing ismade on a side of the duct were the grout is in good condition, butwhere the strands are farther away from the sensor because of bunchingon the opposite side. An indication of the position of the strandswithin the duct is therefore necessary for appropriate interpretation ofelectromagnetic, acoustic, or thermal measurement results. Although theposition of the strands within the duct can be determined using x-rayimaging, such a process is complicated, time consuming, and expensive.

In view of the above discussion, it can be appreciated that it would bedesirable to have an alternative way to determine the position of steelstrands within a tendon used in a post-tensioned segmental structure.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure may be better understood with reference to thefollowing figures. Matching reference numerals designate correspondingparts throughout the figures, which are not necessarily drawn to scale.

FIG. 1 is a schematic view that illustrates an embodiment of a methodfor determining the position of strands within a tendon in apost-tensioned structure.

FIG. 2 is a schematic view of an embodiment of a system for determiningthe position of strands within a tendon in a post-tensioned segmentalstructure.

FIG. 3 is a graph of force as a function of angular position measured bya sensing magnet during experiments.

FIG. 4A is a photograph of a cross-section of a first tendon specimen.

FIG. 4B is a radial plot of strand position generated for the firsttendon specimen of FIG. 4A.

FIG. 5A is a photograph of a cross-section of a second tendon specimen.

FIG. 5B is a radial plot of strand position generated for the secondtendon specimen of FIG. 5A.

DETAILED DESCRIPTION

As described above, it would be desirable to have an alternative way todetermine the position of steel strands within a tendon used in apost-tensioned structure. Disclosed herein are systems and methodssuited for that purpose. More particularly, disclosed are systems andmethods for identifying the distribution of the strands using magneticsensing. In some embodiments, a magnet traverses the circumference ofthe tendon and the force with which it is attracted to the strandswithin the tendon is measured as a function of angular position. Thatforce information can then be used to create a radial plot that providesan indication of the location of the strands within the tendon.

In the following disclosure, various specific embodiments are described.It is to be understood that those embodiments are exampleimplementations of the disclosed inventions and that alternativeembodiments are possible. All such embodiments are intended to fallwithin the scope of this disclosure.

FIG. 1 illustrates in cross-section an example tendon of the type usedin a post-tensioned structure. As is shown in that figure, the tendon iscomprised of an outer duct, multiple steel strands positioned within theduct, and grout that fills the space within the duct not alreadyoccupied by the strands. In the typical case, the duct is made of apolymeric material, the strands are steel cables, and the grout is amixture of cement and water. As is apparent from the figure, the strandsare not evenly distributed across the cross-section of the duct.Instead, the strands are crowded near one side (the top side in FIG. 1)of the duct. This type of crowding is common as the inter-spacing ofstrands can vary along the tendon depending on the proximity ofdeviation blocks, the way in which the strands were threaded duringinitial placement at the time of construction, and deviations from astraight cylindrical shape of the duct as produced or due to gravitydeflection.

As noted above, the distribution of the strands within the duct can beidentified using magnetic sensing. FIG. 1 illustrates an example ofthis. Specifically, FIG. 1 shows a sensing magnet that is positioned inclose proximity to the outer surface of the duct. As is furtherindicated in the figure, the magnet can radially traverse (i.e., rotateabout) the periphery of the tendon (see dashed arrows) for the purposeof measuring the force of attraction between the magnet and the strandsat various angular positions.

FIG. 2 illustrates an example system 10 for determining the position ofstrands within a tendon. As shown in this figure, the system 10 includesa mechanism comprising a ring member 12 that can be temporality mountedto a tendon 14 in a desired position along its length. As before, thetendon 14 includes a duct 16 that surrounds multiple steel strands 18and grout 20. In the illustrated embodiment, the ring member 12 forms acircular track along which a carriage 22 can travel, and thereforerotate around the tendon 14. In the embodiment of FIG. 1, the trackincludes a circular flange 24 with which one or more wheels 26 of thecarriage 22 make contact. In some embodiments, the flange 24 and one ormore of the wheels 26 can comprise gear teeth (not shown) that ensurethat the carriage 16 does not slip as it travels along the ring member12. In further embodiments, one or more of the wheels 20 can be drivenby a motor (not shown) so that such traversal is automated.

As is further indicated in FIG. 2, a sensing magnet 28 is mounted to thecarriage 22. The magnet 28 can travel in a radial direction toward oraway from the tendon 14 depending upon the attractive forces generatedbetween the magnet and the stands 18 of the tendon 14. In theillustrated embodiment, the magnet 28 is coupled to a force sensor 30,such as a force transducer, with a spring 32. In such a case, force ofattraction between the magnet 28 and the strands 18 can be measured. Asis also shown in FIG. 2, the carriage 22 comprises a position sensor 34that can be used to identify the angular position of the carriage 22 onthe ring member 12 (and therefore the angular position along the tendon14) for purposes of correlating the measured forces with the angularpositions. In some embodiments, the sensor 34 comprises an encoderassociated with one of the wheels 26 that determines angular positionbased upon rotation of the wheel.

With further reference to FIG. 2, the carriage 22 and its sensors 30, 34can be placed in electrical communication with a computing device 36,such as a notebook computer or tablet computer, which can store themeasurements and, in some embodiments, determine the positions of thestrands 18 based upon the measurements.

While the system 10 has been described as comprising a single carriage22 and a single sensing magnet 28, it is noted that multiple carriagesand/or magnets could be used, if desired. Furthermore, while a motorizedcarriage 22 has been described, it is noted that the carriage canalternatively be manually displaced along the ring member 12, ifdesired. Moreover, it is noted that although the system 10 has beendescribed as comprising a force sensor, other parameters could be sensedto obtain an indication of the magnetic force applied to the magnet. Forexample, a position sensor that senses displacement of the magnet 28 asit interacts with the spring could be used to obtain an indication ofthe attractive force applied to the magnet.

In use, the ring member 12 can be mounted to the tendon 14 at aparticular position along its length and the carriage 22 can travelalong the ring member and around the tendon. Multiple force measurementscan be obtained at discrete angular positions as the carriage 22 travelsand the angular positions associated with those measurements can berecorded. Alternatively, force and angular position can be continuouslymeasured as the carriage 22 travels. Once the entire circumference ofthe tendon 14 has been traversed, the ring member 12 can be disconnectedfrom the tendon, moved to a new longitudinal position of the tendon, andthe measuring process can be repeated. This process can then be repeatedfor multiple positions along the length of the tendon until all desiredmeasurements have been obtained. Alternatively, the system 10 canoperate in a continuous mode in which it moves along the length of thetendon 14 in a manual or motorized fashion and provides a continuousrecord of output.

For any given longitudinal position of the tendon, the output of themeasurement process is a vector of attractive force values at successiveangular positions. For example, if force is recorded at 10-degreeintervals, a vector with 36 values is obtained. The indication of thestrand layout can then be obtained by deconvolution using the vectorvalues and the knowledge of the strand size, the number of strands, andthe duct wall thickness. The deconvolution can be performed usingprocedures of various degrees of sophistication depending on the needfor accuracy. In its simplest form, the deconvolution can be based uponthe observation that, for a single short magnet with a field thatapproaches that of simple magnetic dipole, the force between a singlestrand and the magnet follows an approximately third power inversedependence with the distance between the magnet and the strand. Theforce vector can then be converted into a distance vector that, whendisplayed in a radial plot, yields an indication of the envelope of thestrand bundle in the tendon cross-section. The precise value of thepower-law exponent (n) can be refined by calibration against informationfrom test specimens with known strand configurations.

Testing of the above-described measurement process and processingtechnique was performed in the laboratory. For practical purposes, afixed magnet was used and short (e.g., 1 foot long) tendon specimenswere rotated relative to the magnet. The specimens had ducts made ofpolyethylene having a 3.5 inch external diameter and a 0.22 inch wallthickness. The ducts contained twelve ½ inch, 7-wire post-tensioningstrands and grout filled the remainder of the interior space of theducts. A ⅝ inch diameter, 3/16 inch thick ceramic magnet withmagnetization in the direction of the main axis was placed with one ofthe flat faces approximately 0.04 inches away from the outer ductsurface. Force measurements were taken at 10 degree intervals with adigital balance coupled to the magnet. A first specimen had a relativelyuniform strand distribution as shown in FIG. 4A and a second specimenhad strands crowded near the top as shown in FIG. 5A. Data outputvectors for the two test specimens are graphically shown in FIG. 3.

Results for the evaluations of the two specimens using the simplifieddeconvolution method are presented in FIGS. 4B and 5B. A value of n=3successfully recovered the general shape of the envelope of the actualstrand pattern in both tendon specimens, but a value of n=2.5, used tocompute the recovered pattern shown in the figures, was found to betterquantitatively approximate the actual boundaries of the envelope.

More sophisticated recovery procedures can be used to identify not onlythe overall envelope of steel placement but also the position ofindividual strands. Those procedures are implementable by a formalsolution of the inverse of the problem of predicting the force profileas function of the strand distribution. The forward problem is amenableto straightforward solution by finite element calculations. As apractical approach to solve the inverse problem, a library of solutionsto the forward problem is prepared for a given tendon arrangement (aspecific number and type of strands in a given duct diameter) covering afinite number of configurations whereby the position of each strand canadopt a number of discretely separated positions (e.g. on a 3 mm squaregrid). Because the grout space in the tendon cross-section is usuallyquite limited (the test specimens, from a research project, were anexception; tendons tend to be more tightly packed), the number offorward solutions to be calculated is limited and is well within thecapabilities of ordinary computing equipment. The data output can thenbe readily compared to the library set of forward solutions by lookupfunctions to minimize fit error and thus identify the library standconfiguration that provides the best match.

A more organized but potentially more challenging approach to solve theinverse problem is to prepare a tractable formulation of the magneticflux distribution in the system using, for example, finite differencemethods and to develop a transfer matrix that relates strand positionsto the force-angle profile. Inversion of the matrix then provides forstructured solution of the inverse problem.

It is noted that the measurement process described above can be alteredin various ways. For example, the strand array can demagnetized prior tomeasurement. If the strands have permanent magnetization from priormagnetic flux tests or other causes, analysis of the results can becompromised. A degaussing step with a moving coil may be used in thosecases and may be built into the examination procedure as a preliminarystep.

As another example, alternative magnet configurations can be used. Along magnet can approximate magnetic monopole behavior at one end withlower magnetic field decay with distance than in the case of a shortdiscrete magnet. This difference can be used to advantage to sample withmore sensitivity the presence of steel deeper into the cross-section ofthe tendon. Similarly, an array of small magnets placed at the end of ahigh magnetic permeability ferrous sheet of material can approximate atwo-dimensional magnetic field configuration with even lower field decaywith distance and consequently has the potential for deeper sampling.The use of near two-dimensional fields is possible because the axis ofindividual strands is usually at a very small angle with respect to themain tendon axis. Therefore, over the short distances sampled by themagnetic array, the cross-section strand pattern changes little.Independent scans performed with various magnetic sensor configurationscan be combined to provide more detailed spatial strand configurationinformation at various depth zones.

As a further example, inductance change measurements can be used. Themethodology commonly used for rebar location, based on inductancechanges of a coil or system of coils when in proximity to steel, can beadapted to the present system in lieu of or as a supplement to permanentmagnet sensors. Application of inductive sensors to post-tensionedtendons and deconvolution of the signal for the application at handalong the lines indicated above may have merit.

The invention claimed is:
 1. A system for determining the position ofstrands in a post-tensioned tendon, the system comprising: a trackadapted to mount to the tendon in a manner in which the track encirclesthe outer circumference of the tendon; and a carriage mounted to thetrack, the carriage supporting a magnet and a sensor that provides anindication of magnetic forces applied to the magnet, the carriage beingpositioned on the track in a manner in which the magnet is placed inclose proximity to an outer surface of the tendon, the carriage beingconfigured to travel along the track so as to rotate the magnet aroundthe outer circumference of the tendon such that circumferential magneticforce readings can be obtained at a discrete position along a length ofthe tendon.
 2. The system of claim 1, wherein the system comprises anarray of magnets.
 3. The system of claim 1, wherein the sensor is aforce sensor that is associated with the magnet.
 4. The system of claim3, wherein the force sensor is a force transducer.
 5. The system ofclaim 3, wherein the force sensor is coupled to the magnet with aspring.
 6. The system of claim 1, wherein the mechanism includes a ringmember that mounts to the tendon.
 7. The system of claim 6, furthercomprising a carriage that supports the magnet, wherein the carriage cantravel along a track defined by the ring member.
 8. The system of claim7, further comprising a motor that drives the carriage along the track.9. The system of claim 1, further comprising a position sensorconfigured to determine the angular position of the magnet relative tothe tendon.
 10. The system of claim 1, further comprising a computingdevice in electrical communication with the sensor configured to recorddata provided by the sensor.
 11. The system of claim 10, wherein thecomputing device is further configured to determine the positions of thestrands based upon the recorded data.
 12. The system of claim 10,wherein the computing device is configured to generate a radial plot ofthe tendon that identifies strand positions.
 13. A method fordetermining the positions of strands in a post-tensioned tendon, themethod comprising: positioning a magnet in close proximity to the outersurface of the tendon; rotating the magnet around the circumference ofthe tendon using a mechanism mounted to the tendon; sensing a parameterindicative of magnetic forces applied to the magnet; and determining thepositions of the strands based upon the sensed parameter.
 14. The methodof claim 13, wherein positioning and moving a magnet comprisespositioning and moving the magnet using a ring member that mounts to thetendon.
 15. The method of claim 13, wherein sensing a parametercomprises sensing magnetic force applied to the magnet.
 16. The methodof claim 15, wherein determining the position of the strands comprisesgenerating a vector of force values at successive angular positions. 17.The method of claim 15, further comprising deconvoluting the vectorforce values to generate a radial plot that provides an indication ofthe location of the strands within the tendon.
 18. The method of claim17, wherein the deconvolution is based on an assumption that the forcebetween a single strand and the magnet follows an approximately thirdpower inverse dependence with the distance between the magnet and thestrand.
 19. The method of claim 13, further comprising demagnetizing thestrands prior to sensing the parameter.
 20. The method of claim 13,further comprising measuring inductance changes of a coil in proximityto the strands.